Multiple-scale perturbation analysis of slowly evolving turbulence

A multiple-scale perturbation expansion is applied to extract a closed system of two equations governing the scalar descriptors of the turbulence energy spectrum from a spectral closure model. The result applies when the length scale and total energy input of a force that maintains a steady state of homogeneous isotropic turbulence are perturbed slowly and the energy spectrum consequently evolves slowly compared to the time scales of the turbulence itself.